On the Distribution Function and Moments of Power Sums With Log-Normal Components

TLDR

An approximate technique is presented to evaluate the mean and variance of power sums with log‑normal components. Exact two‑component moment expressions are derived and recursively applied to compute the sum’s moments, which are then combined with a Gaussian assumption to characterize the cumulative distribution function, matching Monte Carlo simulations across the 1–99 % range. The method yields more accurate mean and variance estimates across a wide variance range, produces a cumulative distribution function that matches Monte Carlo simulations from the 1–99 % range, and offers simple polynomial moment expressions enabling quick, accurate calculations of system performance metrics such as cochannel interference from shadowing.

Abstract

An approximate technique is presented for the evaluation of the mean and variance of the power sums with log-normal components. Exact expressions for the moments with two components are developed and then used in a nested fashion to obtain the moments of the desired sum. The results indicate more accurate estimates of these quantities over a wider range of individual component variances than any previously reported procedure. Coupling our estimates with the Gaussian assumption for the power sum provides a characterization of the cumulative distribution function which agrees remarkably well with a Monte Carlo simulation in the 1 to 99 percent range of the variate. Simple polynomial expressions obtained for the moments lead to an effective analytical tool for various system performance studies. They allow quick and accurate calculation of quantities such as cochannel interference caused by shadowing in mobile telephony.